Flexural resonator element, resonator, oscillator, and electronic device

ABSTRACT

A crystal resonator element include a pair of resonating arms extending from a base, the resonating arms includes a groove, a slope portion is formed in a connection portion of the resonating arms to the base so that a distance between the groove and the outer edge of each of the resonating arms increases as it approaches the base from the resonating arms, and a non-electrode region which extends over a range of areas from a connection portion connected to a first side surface formed along the longitudinal direction of the groove and a connection portion connected to a second side surface facing the first side surface with a bottom portion disposed there between and in which excitation electrodes are not formed is provided in the groove in at least a part of the bottom portion positioned in the slope portion.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a Continuation of U.S. application Ser. No. 13/176,192 filedJul. 5, 2011, which claims priority to Japanese Patent Application No.2010-156576 filed Jul. 9, 2010, the disclosure of which is incorporatedherein by reference in its entirety.

BACKGROUND

1. Technical Field

The present invention relates to a flexural resonator element, and aresonator, an oscillator, and an electronic device each having theflexural resonator element.

2. Related Art

In the related art, the fact that when a flexural resonator element isminiaturized, the Q value decreases and the flexural vibration thereofis disturbed is known. Here, the Q value is a dimensionless numberrepresenting the vibration state, and the higher it is, the more stablythe flexural resonator element vibrates. This results from athermoelastic effect which occurs when a relaxation vibration frequencythat is inversely proportional to the relaxation time up to theequilibrium of temperature through heat transfer approaches a vibrationfrequency of the flexural resonator element. That is, when a flexuralresonator element vibrates in the flexural vibration mode, an elasticdeformation occurs, and the temperature of a compressed surfaceincreases while the temperature of an expanded surface decreases. Thus,a temperature difference occurs in the inner portion of the flexuralresonator element. The flexural vibration is disturbed by relaxationvibration of which the frequency is inversely proportional to therelaxation time up to equilibrium of the temperature difference throughthermal conduction, and the Q value decreases.

In order to address this problem, JP-UM-A-2-32229 (see page 4 line 7 topage 5 line 3) discloses a technique in which a groove or a through-holeis formed in a flexural vibration portion of a flexural resonatorelement to prevent the transfer of generated heat from the compressedsurface of a resonator to the expanded surface, thus suppressing changesin the Q value resulting from the thermoelastic effect.

Moreover, JP-A-2009-27711 (see FIG. 1 and FIG. 1a) discloses apiezoelectric tuning fork-type resonator (hereinafter referred to as aflexural resonator element). The flexural resonator element includesabase from which first and second parallel resonating arms extend, anenlarged portion (hereinafter referred to as a weight portion) having aflipper-like shape forming the free end of each of the resonating arms,and an excitation electrode for resonating each resonating arm, and agroove formed on at least one of the top or bottom surfaces of each ofthe resonating arms.

In the flexural resonator element having the groove as disclosed inJP-UM-A-2-32229, the groove prevents the diffusion (thermal conduction)of the heat generated by flexural vibration. Thus, it is possible tosuppress thermoelastic loss which is a loss of vibration energy causedby thermal conduction occurring between the contracted portion and theexpanded portion of a flexural resonator element resonating in theflexural vibration mode.

However, the flexural resonator element having the groove as describedabove has a portion which is disposed in a connection portion connectedto the base of the resonating arm and in which larger stress occurs dueto flexural vibration than other portions of the resonating arm. Thus, alarge temperature difference occurs in the flexural resonator elementwhen the temperature rises and falls.

Moreover, in the groove positioned in the connection portion of theresonating arm connected to the base, an excitation electrode iscontinuously formed on the surface thereof so as to extend from one sidein the width direction of the resonating arm to the other side.Therefore, thermal conduction in the connection portion of theresonating arm connected to the base is accelerated by the excitationelectrode that is formed of a metal having high thermal conductivity andformed on the groove in the connection portion. The present inventor hasfound a problem wherein the thermoelastic loss increases and the Q valuedecreases.

According to FIG. 1 of JP-A-2009-27711, the flexural resonator elementhas a slope portion (tapered portion) which is formed between theresonating arm and the base so that the distance between the groove andthe outer edge of the resonating arm increases as it approaches the basefrom the resonating arm in plan view.

According to FIG. 1 and FIG. 1a of JP-A-2009-27711, in the flexuralresonator element, the excitation electrode formed in the groove extendsup to a range corresponding to the connection portion and is formed inthe inner wall of the groove so as to be continuous from one end in thewidth direction of the resonating arm to the other end thereof.

SUMMARY

The present inventors found that, due to this configuration, in theflexural resonator element, the thermal conduction in the slope portionwhich does not contribute to excitation of the flexural vibration of theresonating arm is accelerated by the excitation electrode that is formedof a metal having high thermal conductivity and formed in the bottomportion of the groove corresponding to the slope portion, and as aresult, the thermoelastic loss increases and the Q value decreases.

An advantage of some aspects of the invention is to solve at least apart of the problems described above and the invention can beimplemented as the following forms or application examples.

APPLICATION EXAMPLE 1

According to this application example of the invention, there isprovided a flexural resonator element including: a base; and aresonating arm which extends from the base and has a connection portiondisposed close to the base and connected to the base and which vibratesin a flexural vibration mode, wherein the resonating arm has a groovewhich is formed on a principal surface thereof along the longitudinaldirection of the resonating arm to be continuous to the connectionportion, wherein an excitation electrode is disposed in the groove, andwherein a part of the groove is disposed in the connection portion, andhas a non-electrode region in which the excitation electrode is notformed.

According to this configuration, in the flexural resonator element, apart of the groove is disposed in the connection portion, and has thenon-electrode region in which the excitation electrode is not formed.

As a result, in the flexural resonator element, the thermal conductivityin the non-electrode region of the groove disposed in the connectionportion of the resonating arm decreases as compared to a case in whichthe excitation electrode is formed. Thus, for example, the transfer ofheat from the contracted portion during the flexural vibration to theexpanded portion is slowed down. Accordingly, it is possible to suppressthe thermoelastic loss of the connection portion.

Therefore, in the flexural resonator element, it is possible to improvethe Q value as compared to a case in which an electrode is formed in thegroove disposed in the connection portion of the resonating arm.

APPLICATION EXAMPLE 2

In the flexural resonator element of the above application example, itis preferable that the resonating arm has a shape such that the width ofthe connection portion between the groove and the outer edge of theresonating arm on the principal surface increases as it approaches thebase from the tip end of the resonating arm.

According to this configuration, in the flexural resonator element, thedistance of the connection portion between the groove and the outer edgeof the resonating arm on the principal surface increases as itapproaches the base from the tip end of the resonating arm, and thenon-electrode region in which the excitation electrode is not formed isprovided in at least a part of the groove that is disposed in theconnection portion.

As a result, in the flexural resonator element, due to the reasonsdescribed above, it is possible to suppress the thermoelastic loss ofthe connection portion and to improve the Q value.

APPLICATION EXAMPLE 3

In the flexural resonator element of the above application example, itis preferable that the excitation electrode has first and secondexcitation electrode portions, the first excitation electrode portion isdisposed on one side in the width direction of the resonating arm in theinner wall of the part of the groove, and the second excitationelectrode portion is disposed on the other side, and the non-electroderegion is disposed between the first and second excitation electrodeportions.

According to this configuration, in the flexural resonator element, thefirst excitation electrode portion is disposed on one side in the widthdirection of the resonating arm in the inner wall of the part of thegroove, and the second excitation electrode portion is disposed on theother side. Therefore, it is possible to decrease the CI (CrystalImpedance) value (which is a value serving as an indicator of thelikelihood of oscillation, and the lower it is, the more the flexuralresonator element is likely to oscillate) as compared to a case in whichthe excitation electrode is not formed in the groove disposed in theconnection portion.

APPLICATION EXAMPLE 4

In the flexural resonator element of the above application example, itis preferable that the groove includes: a first side surface extendingalong the longitudinal direction of the resonating arm; a second sidesurface extending along the longitudinal direction of the resonatingarm; and a bottom portion connecting the first and second side surfacesand forming the bottom of the groove, a part of the bottom portion isdisposed in the connection portion, and the non-electrode region isprovided in at least a part thereof, and the groove has the excitationelectrode which is disposed on the entire area of the first and secondside surfaces in plan view.

According to this configuration, the flexural resonator element has theexcitation electrode which is formed on the entire area of the first andsecond side surfaces of the groove. Therefore, it is possible todecrease the CI value as compared to a case described later in which theexcitation electrode is formed in a part of the first and second sidesurfaces of the groove.

Therefore, in the flexural resonator element, it is possible to improvethe Q value as compared to a case in which the excitation electrode isformed in a part of the first and second side surfaces of the groove.

APPLICATION EXAMPLE 5

In the flexural resonator element of the above application example, itis preferable that the groove includes: a first side surface extendingalong the longitudinal direction of the resonating arm; a second sidesurface extending along the longitudinal direction of the resonatingarm; and a bottom portion connecting the first and second side surfacesand forming the bottom of the groove, a part of the bottom portion isdisposed in the connection portion, and the non-electrode region isprovided in at least a part thereof, and the groove has the excitationelectrode which is disposed in a part of the first side surface and apart of the second side surface in plan view.

According to this configuration, in the flexural resonator element, theexcitation electrode is formed in a part of the first and second sidesurfaces of the groove. Therefore, it is possible to decrease the loadcapacitance sensitivity (which indicates the amount of change in thefrequency with changes in the load capacitance, and the lower it is, theless the frequency is likely to change) as compared to theabove-described case in which the excitation electrode is formed on theentire area of the first and second side surfaces.

Therefore, in the flexural resonator element, it is possible to suppresschanges in the frequency resulting, for example, from floatingcapacitance or the like as compared to a case in which the excitationelectrode is formed on the entire area of the first and second sidesurfaces of the groove.

APPLICATION EXAMPLE 6

In the flexural resonator element of the above application example, itis preferable that the bottom portion disposed in the connection portionhas a sloped surface in which the depth of the groove increases as itapproaches the tip end of the resonating arm from the base, and thenon-electrode region is provided in the sloped surface.

According to this configuration, in the flexural resonator element, thebottom portion of the groove has the sloped surface which is inclined sothat the depth of the groove increases as it approaches the tip end ofthe resonating arm from the base, and the non-electrode region isprovided in the sloped surface. Therefore, for example, when anelectrode protective film (resist) is subjected to patterning usingphotolithography to form the non-electrode region, it is possible toprevent a non-exposure portion (the first and second side surfaces orthe like) from being irradiated with exposure light through reflectionof light.

APPLICATION EXAMPLE 7

In the flexural resonator element of the above application example, itis preferable that the resonating arm includes an arm portion which isdisposed close to the base, and a weight portion which is disposedcloser to a tip end of the resonating arm than the arm portion.

According to this configuration, in the flexural resonator element, theresonating arm includes an arm portion which is disposed close to thebase, and a weight portion which is disposed closer to a tip end of theresonating arm than the arm portion. Through the effect of improving theQ value by the weight portion which increases the inertial mass, it ispossible to shorten the resonating arm while maintaining the Q value,for example.

Therefore, in the flexural resonator element, it is possible to achievefurther miniaturization while maintaining the Q value.

On the other hand, when the weight portion is provided in the flexuralresonator element, for example, the amount of deformation of theconnection portion during flexural vibration, for example, increases ascompared to a configuration in which no weight portion is provided. Thatis, the heat generated increases.

However, in the flexural resonator element, the thermal conductivity inthe non-electrode region in the bottom portion of the groovecorresponding to the slope portion decreases as compared to a case inwhich an electrode is formed. Thus, the transfer of heat from thecontracted portion to the expanded portion is slowed down. Accordingly,the thermoelastic loss in the connection portion can be suppressed moreeffectively when the weight portion is provided.

APPLICATION EXAMPLE 8

In the flexural resonator element of the above application example, itis preferable that the flexural resonator element includes a pluralityof the resonating arms, and the plurality of resonator arms and the baseform a tuning fork.

According to this configuration, the flexural resonator element includesa plurality of the resonating arms and the base which form a tuningfork. Thus, it is possible to provide a tuning fork-type flexuralresonator element having the effects of any one of the above-mentionedapplication examples.

APPLICATION EXAMPLE 9

According to this application example of the invention, there isprovided a resonator including the flexural resonator element of any oneof the above-mentioned application examples and a package thataccommodates the flexural resonator element.

According to this configuration, since the resonator includes theflexural resonator element of any one of the above-mentioned applicationexamples, it is possible to provide a resonator having the effects ofany one of the above-mentioned application examples.

APPLICATION EXAMPLE 10

According to this application example of the invention, there isprovided an oscillator including the flexural resonator element of anyone of the above-mentioned application examples and a circuit elementthat has a circuit oscillating the flexural resonator element.

According to this configuration, since the oscillator includes theflexural resonator element of any one of the above-mentioned applicationexamples, it is possible to provide an oscillator having the effects ofany one of the above-mentioned application examples.

APPLICATION EXAMPLE 11

According to this application example of the invention, there isprovided an electronic device including the flexural resonator elementof any one of the above-mentioned application examples.

According to this configuration, since the electronic device includesthe flexural resonator element of any one of the above-mentionedapplication examples, it is possible to provide an electronic devicehaving the effects of any one of the above-mentioned applicationexamples.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be described with reference to the accompanyingdrawings, wherein like numbers reference like elements.

FIGS. 1A to 1C are schematic diagrams showing a simplified configurationof a flexural resonator element according to a first embodiment, inwhich FIG. 1A is a plan view, and FIGS. 1B and 1C are cross-sectionalviews of FIG. 1A.

FIG. 2 is a diagram showing the relationship between a relaxationfrequency of the flexural resonator element and the minimum value of theQ value.

FIGS. 3A and 3B are schematic diagrams showing a simplifiedconfiguration of a flexural resonator element according to a firstmodification, in which FIG. 3A is a plan view, and FIG. 3B is across-sectional view of FIG. 3A.

FIGS. 4A and 4B are schematic diagrams showing a simplifiedconfiguration of a flexural resonator element according to a secondmodification, in which FIG. 4A is a plan view, and FIG. 4B is across-sectional view of FIG. 4A.

FIG. 5 is a schematic cross-sectional view of a main part of a flexuralresonator element according to a third modification.

FIGS. 6A and 6B are schematic diagrams showing a simplifiedconfiguration of a resonator according to a second embodiment, in whichFIG. 6A is a plan view, and FIG. 6B is a cross-sectional view of FIG.6A.

FIGS. 7A and 7B are schematic diagrams showing a simplifiedconfiguration of an oscillator according to a third embodiment, in whichFIG. 7A is a plan view, and FIG. 7B is a cross-sectional view of FIG.7A.

FIG. 8 is a schematic perspective view showing an electronic deviceaccording to a fourth embodiment.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

Hereinafter, embodiments of the invention will be described withreference to the drawings.

First Embodiment

FIGS. 1A and 1B are schematic diagrams showing a simplifiedconfiguration of a flexural resonator element according to a firstembodiment, in which FIG. 1A is a plan view, FIG. 1B is across-sectional view taken along the line A-A in FIG. 1A, and FIG. 1C isa cross-sectional view taken along the line B-B in FIG. 1A.

In FIG. 1A, hatching or shading is added to electrode parts for the sakeof convenience, and the electrode parts are simplified or partiallyomitted for better understanding of the drawing. Moreover, in FIG. 1C,the cross-section of a part (supporting portion) of the constituentelements is omitted.

As shown in FIGS. 1A to 1C, a crystal resonator element 1 used as aflexural resonator element is a flexural resonator element of which theouter shape is formed by photolithographically etching (wet-etching) awafer-shaped crystal substrate which is used as a base material andwhich is cut, for example, from crystal ore, at predetermined angles.

The crystal resonator element 1 includes a base 11, a pair of resonatingarms 12 and 13 extending approximately in parallel from the base 11, apair of notches 14 which is notched from both sides of the base 11 in adirection (the left-right direction of the drawing sheet) crossing theextension direction of the resonating arms 12 and 13, namely in thewidth direction of the resonating arms 12 and 13, and a pair ofsupporting portions 15 protruding from the base 11 in the left-rightdirection of the drawing sheet, bent approximately at a right angletowards the resonating arms 12 and 13, and extending along theresonating arms 12 and 13.

The pair of resonating arms 12 and 13 includes an arm portion 16positioned close to the base 11 and a weight portion 17 positionedcloser to the tip end of each of the resonating arms 12 and 13 than thearm portion 16 and having a larger width than the arm portion 16.

Moreover, the pair of resonating arms 12 and 13 includes a groove 18which is formed on principal surfaces 10 a and 10 b facing each other soas to extend along the longitudinal direction of the pair of resonatingarms 12 and 13 and which is cut along the arrangement direction (theleft-right direction of the drawing sheet) of the pair of resonatingarms 12 and 13 so that the resonating arms 12 and 13 have anapproximately H-shape in cross-sectional view.

The crystal resonator element 1 includes a slope portion 19 which isformed in a connection portion adjacent to the base 11 so that adistance between the groove 18 and the outer edge of each of theresonating arms 12 and 13 increases as it approaches the base 11 fromthe resonating arms 12 and 13 in plan view.

The crystal resonator element 1 includes excitation electrodes 20 and 21which are formed (disposed) on the groove 18 of the pair of resonatingarms 12 and 13, the principal surfaces 10 a and 10 b, and the mutuallyfacing side surfaces 12 a and 12 b, and 13 a and 13 b of the pair ofresonating arms 12 and 13.

Next, the excitation electrodes 20 and 21 formed on the groove 18 willbe described.

As shown in FIG. 1B, the groove 18 includes a bottom portion 18 c, afirst side surface 18 a that is positioned on one side in the widthdirection of the resonating arms 12 and 13 with respect to the bottomportion 18 c and formed along the longitudinal direction of theresonating arms 12 and 13, and a second side surface 18 b that ispositioned on the other side in the width direction of the resonatingarms 12 and 13 with respect to the bottom portion 18 c and formed alongthe longitudinal direction of the resonating arms 12 and 13.

Moreover, the excitation electrodes 20 and 21 of the groove 18 in thearm portion 16 are formed to be continuous to the first side surface 18a formed along the longitudinal direction of the groove 18, the bottomportion 18 c, and the second side surface 18 b facing the first sidesurface 18 a with the bottom portion 18 c disposed therebetween.

On the other hand, as shown in FIG. 1C, a non-electrode region whichextends over a range of areas from a connection portion 18 d connectedto the first side surface 18 a and a connection portion 18 e connectedto the second side surface 18 b and in which the excitation electrodes20 and 21 are not formed is provided in at least a part of the bottomportion 18 c positioned in the slope portion 19. Here, the expression “apart” corresponds to “a part of the groove” described in the applicationexamples of the invention, the non-electrode region is provided in theentire bottom portion 18 c positioned in the slope portion 19. Thenon-electrode region is a portion which is not shaded in FIG. 1A asdenoted by reference numeral 18 c.

First excitation electrode portions 20 a and 21 a which are part of theexcitation electrodes 20 and 21 are formed (disposed) on the first sidesurfaces 18 a positioned in the slope portions 19. Second excitationelectrode portions 20 b and 21 b which are part of the excitationelectrodes 20 and 21 are formed (disposed) on the second side surfaces18 b positioned in the slope portions 19.

In the crystal resonator element 1, the excitation electrodes 20 and 21are formed on the entire area of the first and second side surfaces 18 aand 18 b of the groove 18.

As shown in FIGS. 1A to 1C, the crystal resonator element 1 includes thebase 11 and the pair of resonating arms 12 and 13 which form a tuningfork, whereby a tuning fork-type crystal resonator element used as atuning fork-type flexural resonator element is obtained. The crystalresonator element 1 is fixed to an external member such as a package ata predetermined position of each of the supporting portions 15.

In the crystal resonator element 1, when an external driving signal isapplied to the excitation electrodes 20 and 21 formed on the pair ofresonating arms 12 and 13, the pair of resonating arms 12 and 13alternately vibrate (resonate) in the flexural vibration mode at apredetermined frequency (for example, 32.768 kHz) in the directionsindicated by the arrows C and D.

Next, the excitation electrodes 20 and 21 formed on the pair ofresonating arms 12 and 13 will be described in detail.

On the pair of resonating arms 12 and 13, the excitation electrodes 20and 21 to which driving signals different in the polarity of the appliedpotential from each other are applied from the outside are formed.

Therefore, the excitation electrodes 20 and 21 are formed to be spacedfrom each other so that they are not short-circuited.

As shown in FIGS. 1B and 1C, the excitation electrode 20 is formed onthe groove 18 of the resonating arm 12, and the excitation electrode 21is formed on both side surfaces 12 a and 12 b of the resonating arm 12.

The excitation electrodes 21 on both side surfaces 12 a and 12 b of theresonating arm 12 are connected to each other by a connection electrode22 (see FIG. 1A) formed on the weight portion 17.

On the other hand, the excitation electrode 21 is formed on the groove18 of the resonating arm 13, and the excitation electrode 20 is formedon both side surfaces 13 a and 13 b of the resonating arm 13.

The excitation electrodes 20 on both side surfaces 13 a and 13 b of theresonating arm 13 are connected to each other by a connection electrode23 (see FIG. 1A) formed on the weight portion 17.

The excitation electrode 20 on the principal surface 10 a side of thegroove 18 of the resonating arm 12 and the excitation electrode 20 onthe principal surface 10 b side are connected to each other by theexcitation electrodes 20 formed on both side surfaces 13 a and 13 b ofthe resonating arm 13.

On the other hand, the excitation electrode 21 on the principal surface10 a side of the groove 18 of the resonating arm 13 and the excitationelectrode 21 on the principal surface 10 b side are connected to eachother by the excitation electrodes 21 formed on both side surfaces 12 aand 12 b of the resonating arm 12.

As shown in FIG. 1A, the excitation electrodes 20 and 21 are led out upto the supporting portions 15 through the base 11, and the lead-outportions serve as mount electrodes 20 c and 21 c which are used when thecrystal resonator element 1 is fixed to the external member such as apackage. The mount electrodes 20 c and 21 c are formed on both principalsurfaces 10 a and 10 b.

Next, an overview of a method of forming the excitation electrodes 20and 21 will be described.

The excitation electrodes 20 and 21 are formed in a desired electrodepattern shape by the following steps. First, an electrode material suchas Ni, Cr, Au, Ag, Al, or Cu is applied to approximately the entiresurface of the crystal resonator element 1 by a method such asdeposition or sputtering. Subsequently, a photosensitive resist isapplied so as to cover the applied electrode material and is subjectedto exposure and patterning in accordance with a desired electrodepattern shape using a photolithography technique. After that,unnecessary exposed portions of the electrode material are removed byetching, whereby the excitation electrodes 20 and 21 having a desiredelectrode pattern shape are obtained.

Moreover, thermal conductivity of a quartz crystal is about 6.2 to about10.4 W/(m·K), and thermal conductivity of Au, for example, used as theelectrode material of the excitation electrodes 20 and 21 is about 315W/(m·K) which is much larger than that of a quartz crystal. The same canbe said for the other electrode materials (Ni, Cr, and the like).

Next, the thermoelastic loss and the relaxation frequency will bedescribed.

For the sake of simplicity, the description will be provided with regardto one resonating arm 12. When the crystal resonator element 1 is in theresonating state, and the resonating arm 12 is vibrated toward one sidein the width direction thereof, tensile stress acts on one side in thewidth direction of the resonating arm 12 and compressive stress acts onthe other side. Generally, the tensile stress and compressive stressacting on the connection portion of the resonating arm 12 adjacent tothe base 11 are larger than the stresses acting on the tip end of theresonating arm 12.

At that time, the temperature increases in the regions where compressivestress acts, and decreases in the regions where tensile stress acts.

The crystal resonator element 1 loses vibration energy due to heattransfer (thermal conduction) occurring due to equilibration oftemperature between the contracted portion of the resonating arm 12resonating in the flexural vibration mode where compressive stress actsand the expanded portion where tensile stress acts.

A decrease in the Q value caused by such thermal conduction is referredto as thermoelastic loss.

From the relationship between deformation and stress which is well-knownas a phenomenon of internal friction of a solid generally occurring dueto a temperature difference, the thermoelastic loss is described asfollows. In a flexural vibration-mode resonator element, when thevibration frequency changes, the Q value reaches the minimum at arelaxation vibration frequency fm=½πτ (here, π is the circular constant,and τ is the relaxation time).

The relationship between the Q value and the frequency is generallyexpressed as a curve F in FIG. 2, in which the curve F represents therelationship between the relaxation frequency of the flexural resonatorelement and the minimum value of the Q value. In the drawing, thefrequency at which the Q value reaches the minimum Q0 is a thermalrelaxation frequency f0 (=½πτ).

Moreover, a region (1<f/f0) on the high frequency side in relation to aboundary of f/f0=1 is an adiabatic region, and a region (f/f0<1) on thelow frequency side in relation to the boundary is an isothermal region.

When the groove 18 is formed in the resonating arms 12 and 13 of thecrystal resonator element 1, a thermal conduction path between thecontracted portion and the expanded portion of the resonating arms 12and 13 is narrowed in the midway by the groove 18. Thus, in the crystalresonator element 1, a relaxation time τ up to the equilibration of thetemperature of the contracted portion and the expanded portionincreases.

Therefore, in the crystal resonator element 1, since the groove 18 isformed, in the adiabatic region shown in FIG. 2, the shape of the curveF itself does not change, but with a decrease of the thermal relaxationfrequency f0, the curve F shifts to the position of a curve F1 in thelower frequency direction. The curve F1 shows a state in which noelectrode (excitation electrode 20 or 21) is formed in the groove 18.

As a result, in the crystal resonator element 1, the Q value increasesas indicated by the arrow a.

However, in the crystal resonator element 1, when the excitationelectrodes 20 and 21 are formed in the groove 18, the curve F shifts tothe position of a curve F2, and the Q value decreases as indicated bythe arrow b.

A thermal conduction path formed by the excitation electrodes 20 and 21can be considered as one of the reasons thereof.

That is, a conductive material such as an electrode material has higherthermal conductivity than a quartz crystal which is a piezoelectricmaterial used as the base material of the crystal resonator element 1.In such a conductive material, electrons as well as phonons of metalcarry thermal energy.

Specifically, in the crystal resonator element 1, since thermalconduction is carried out by the excitation electrodes 20 and 21 formedon the groove 18 as well as a quartz crystal, it is considered that therelaxation time τ decreases, and with an increase of the thermalrelaxation frequency f0, the curve F shifts to the position of the curveF2 in the higher frequency direction.

The crystal resonator element 1 of the first embodiment is designed tooperate in a region in which the thermoelastic loss is in the adiabaticregion, namely a high-frequency region in which the value of fr/f0satisfies a relation of 1<fr/f0 where fr is the mechanical resonancefrequency of a resonating body and f0 is the thermal relaxationfrequency of a simple resonating body. Here, the simple resonating bodymeans a resonating body on which no metal film or the like such as theexcitation electrodes 20 and 21 is formed. For example, when a quartzcrystal is used as the material of the resonating body, a simpleresonating body means a resonating body on which no material other thanthe quartz crystal is formed.

Generally, a thermal relaxation frequency fm is calculated by Equation(1) below.fm=πk/(2ρCpa ²)  (1)

Here, π is the circular constant, k is a thermal conductivity in theresonating direction of a resonating arm, ρ is a mass density of theresonating arm, C_(p) is heat capacity of the resonating arm, and a isthe width in the resonating direction of the resonating arm.

When the constants of the material of the resonating arm are substitutedinto the thermal conductivity k, the mass density ρ, and the heatcapacity C_(p) in Equation 1, the obtained thermal relaxation frequencyfm becomes the thermal relaxation frequency when no groove is formed inthe resonating arm.

As described above, in the crystal resonator element 1 of the firstembodiment, the non-electrode region which extends over a range of areasfrom the connection portion 18 d connected to the first side surface 18a and the connection portion 18 e connected to the second side surface18 b and in which the excitation electrodes 20 and 21 are not formed isprovided in at least a part of the bottom portion 18 c of the groove 18corresponding to the slope portion 19.

As a result, in the crystal resonator element 1 operating in theadiabatic region, the thermal conductivity in the non-electrode regionof the bottom portion 18 c of the groove 18 corresponding to the slopeportion 19 decreases as compared to a case in which the excitationelectrodes 20 and 21 are formed. Thus, the transfer of heat from thecontracted portion (for example, the first side surface 18 a side)during the flexural vibration to the expanded portion (for example, thesecond side surface 18 b side) is slowed down. Accordingly, it ispossible to suppress the thermoelastic loss of the slope portion 19.

Therefore, in the crystal resonator element 1, it is possible to improvethe Q value as compared to a case in which the excitation electrodes 20and 21 are formed in the bottom portion 18 c of the groove 18corresponding to the slope portion 19.

In the crystal resonator element 1, in order to obtain the effects moresecurely, as shown in FIG. 1A, it is preferable that the non-electroderegion is provided in the entire range of the bottom portion 18 c of thegroove 18 corresponding to the slope portion 19.

Since the crystal resonator element 1 has the excitation electrodes 20and 21 which are formed on the entire area of the first and second sidesurfaces 18 a and 18 b of the groove 18, it is possible to decrease theCI value as compared to a case described later in which the excitationelectrodes 20 and 21 are formed in part of the first and second sidesurfaces 18 a and 18 b of the groove 18.

Therefore, in the crystal resonator element 1, it is possible to improvethe Q value as compared to a case in which the excitation electrodes 20and 21 are formed in part of the first and second side surfaces 18 a and18 b of the groove 18.

Moreover, in the crystal resonator element 1, the resonating arms 12 and13 include the arm portion 16 which is disposed close to the base 11,and the weight portion 17 which is disposed closer to the tip end ofeach of the resonating arms than the arm portion 16 and which has alarger width than the arm portion 16. Through the effect of improvingthe Q value by the weight portion 17 which increases the inertial mass,it is possible to shorten the resonating arms 12 and 13 whilemaintaining the Q value, for example.

Therefore, in the crystal resonator element 1, it is possible to achievefurther miniaturization while maintaining the Q value.

On the other hand, when the weight portion 17 is provided in the crystalresonator element 1, the amount of deformation during flexural vibrationincreases as compared to a configuration in which no weight portion 17is provided. That is, the heat generated increases.

However, in the crystal resonator element 1, the thermal conductivity inthe non-electrode region of the bottom portion 18 c of the groove 18corresponding to the slope portion 19 decreases as compared to a case inwhich the excitation electrodes 20 and 21 are formed. Thus, the transferof heat from the contracted portion to the expanded portion is sloweddown. Accordingly, the thermoelastic loss of the slope portion 19 can besuppressed more effectively when the weight portion 17 is provided.

Moreover, the crystal resonator element 1 includes a pair (two) ofresonating arms 12 and 13 and the base 11 which form a tuning fork.Thus, it is possible to provide a tuning fork-type crystal resonatorelement having the above-described effects.

Next, modifications of the first embodiment will be described.

First Modification

FIGS. 3A and 3B are schematic diagrams showing a simplifiedconfiguration of a flexural resonator element according to a firstmodification, in which FIG. 3A is a plan view, and FIG. 3B is across-sectional view taken along the line E-E in FIG. 3A. The sameportions as those of the first embodiment will be denoted by the samereference numerals, detailed description thereof will be omitted, andthose portions different from those of the first embodiment will bedescribed.

As shown in FIGS. 3A and 3B, in a crystal resonator element 2 as aflexural resonator element of the first embodiment, the excitationelectrodes 20 and 21 are not formed in a range L1 of areas of the firstand second side surfaces 18 a and 18 b of the groove 18 corresponding tothe slope portion 19.

In other words, the crystal resonator element 2 includes the excitationelectrodes 20 and 21 which are formed in part of the first and secondside surfaces 18 a and 18 b of the groove 18.

According to this configuration, since the crystal resonator element 2includes the excitation electrodes 20 and 21 which are formed in part ofthe first and second side surfaces 18 a and 18 b of the groove 18, thearea of the excitation electrodes 20 and 21 in the first and second sidesurfaces 18 a and 18 b of the groove 18 is smaller than theabove-described case in which the excitation electrodes 20 and 21 areformed on the entire area of the first and second side surfaces 18 a and18 b.

Due to this configuration, since the motional capacitance of the crystalresonator element 2 decreases, it is possible to decrease the loadcapacitance sensitivity.

Therefore, in the crystal resonator element 2, it is possible tosuppress changes in the frequency resulting, for example, from floatingcapacitance or the like as compared to a case in which the excitationelectrodes 20 and 21 are formed on the entire area of the first andsecond side surfaces 18 a and 18 b of the groove 18.

Second Modification

FIGS. 4A and 4B are schematic diagrams showing a simplifiedconfiguration of a flexural resonator element according to a secondmodification, in which FIG. 4A is a plan view, and FIG. 4B is across-sectional view taken along the line F-F in FIG. 4A. The sameportions as those of the first embodiment will be denoted by the samereference numerals, detailed description thereof will be omitted, andthose portions different from those of the first embodiment will bedescribed.

As shown in FIGS. 4A and 4B, in a crystal resonator element 3 as aflexural resonator element of the second embodiment, the excitationelectrodes 20 and 21 are not formed in a partial range L2 of areas ofthe first and second side surfaces 18 a and 18 b and the bottom portion18 c disposed close to the weight portion 17 of the groove 18 as well asin the range L1 of areas of the first and second side surfaces 18 a and18 b of the groove 18 corresponding to the slope portion 19 described inthe first modification.

According to this configuration, in the crystal resonator element 3, thearea of the excitation electrodes 20 and 21 in the first and second sidesurfaces 18 a and 18 b of the groove 18 decreases further as compared tothe first embodiment and the first modification.

Due to this configuration, since the motional capacitance of the crystalresonator element 3 decreases further, it is possible to furtherdecrease the load capacitance sensitivity.

Therefore, in the crystal resonator element 3, it is possible to furthersuppress changes in the frequency resulting, for example, from floatingcapacitance or the like as compared to the first embodiment and thefirst modification.

In addition, since the excitation electrodes 20 and 21 are not formed inthe bottom portion 18 c in the partial range L2 of areas on the weightportion 17 side of the groove 18, the transfer of heat from thecontracted portion (for example, the first side surface 18 a side)during the flexural vibration in the range L2 to the expanded portion(for example, the second side surface 18 b side) is slowed down.Accordingly, it is possible to suppress the thermoelastic loss.

Therefore, in the crystal resonator element 3, it is possible to furtherimprove the Q value as compared to the first embodiment and the firstmodification.

Third Modification

FIG. 5 is a schematic cross-sectional view of a main part of a flexuralresonator element according to a third modification.

FIG. 5 is a cross-sectional view of a main part on the base 11 side ofthe groove 18, of a crystal resonator element 4 as a flexural resonatorelement according to the third modification taken along the extensiondirection of the resonating arms 12 and 13.

The other configurations of the crystal resonator element 4 other thanthe groove 18 shown in FIG. 5 are the same as those of the firstembodiment and the respective modifications.

As shown in FIG. 5, when the groove 18 is formed by wet-etching, forexample, the bottom portion 18 c of the groove 18 of the crystalresonator element 4 corresponding to the slope portion 19 has a slopedsurface 18 f which is inclined so that the depth of the groove 18increases as it approaches the tip ends of the resonating arms 12 and 13from the base 11 side.

Moreover, the bottom portion 16 c of the groove 18 of the crystalresonator element 4 corresponding to the slope portion 19 has anon-electrode region which is provided on the sloped surface 18 f.

Moreover, the sloped surface 18 f is not inclined toward the first orsecond side surface 18 a or 18 b when the sloped surface 18 f is cutalong the direction crossing the extension direction of the resonatingarms 12 and 13.

According to this configuration, in the crystal resonator element 4, thebottom portion 18 c of the groove 18 of the crystal resonator element 4corresponding to the slope portion 19 has the sloped surface 18 f whichis inclined so that the depth of the groove 18 increases as itapproaches the tip ends of the resonating arms 12 and 13 from the base11 side, and the non-electrode region is provided on the sloped surface18 f. When a resist is subjected to patterning using photolithography toform the electrode pattern of the excitation electrodes 20 and 21, it ispossible to prevent a non-exposure portion (the first and second sidesurfaces 18 a and 18 b or the like) from being irradiated with exposurelight through reflection of light.

Specifically, exposure light O illuminated from above the groove 18toward the sloped surface 18 f is reflected from the sloped surface 18 fof the bottom portion 18 c. However, since the sloped surface 18 f isinclined so that the depth of the groove 18 increases as it approachesthe tip ends of the resonating arms 12 and 13 from the base 11, thereflected light is reflected at an angle corresponding to its incidenceangle toward the tip ends of the resonating arms 12 and 13 along theextension direction of the resonating arms 12 and 13.

As a result, in the crystal resonator element 4, it is possible toprevent the non-exposure portion (the first and second side surfaces 18a and 18 b or the like) from being irradiated with the exposure light Othrough reflection of light when the resist is subjected to patterningusing photolithography to form the electrode pattern of the excitationelectrodes 20 and 21.

Here, in the sloped surface 18 f of the bottom portion 18 c, thepositions of both ends in the left-right direction of the drawing sheetin FIG. 5 are not necessarily identical to the positions of both ends ofthe slope portion 19. For example, the end of the sloped surface 18 f ofthe bottom portion 18 c on the tip end side (the left side of thedrawing sheet) of the resonating arms 12 and 13 may be outside the slopeportion 19 and may be within the slope portion 19.

Second Embodiment

Next, a resonator having the crystal resonator element described abovewill be described as a second embodiment.

FIGS. 6A and 6B are schematic diagrams showing a simplifiedconfiguration of a resonator according to the second embodiment, inwhich FIG. 6A is a plan view, and FIG. 6B is a cross-sectional viewtaken along the line G-G in FIG. 6A. The electrodes of the crystalresonator element are not illustrated for better understanding of thedrawings.

As shown in FIGS. 6A and 6B, a crystal resonator 5 as a resonatorincludes the crystal resonator element 1 of the first embodiment and apackage 80 that accommodates the crystal resonator element 1.

The package 80 includes a package base 81, a shim ring 82, a cover 85,and the like.

The package base 81 has a recess so that the crystal resonator element 1can be accommodated therein, and connection pads 88 connected to themount electrodes 20 c and 21 c (not shown; see FIGS. 1A and 1B) of thecrystal resonator element 1 are provided in the recess.

The connection pads 88 are connected to wirings inside the package base81 so as to be electrically connected to an external connection terminal83 provided at the periphery of the package base 81.

The shim ring 82 is provided around the recess of the package base 81. Athrough-hole 86 is provided on the bottom of the package base 81.

The crystal resonator element 1 is attached to the connection pads 88 ofthe package base 81 by a conductive adhesive 84. In the package 80, thecover 85 covering the recess of the package base 81 is shim-welded tothe shim ring 82.

A sealing material 87 made from metal is filled in the through-hole 86of the package base 81. The sealing material 87 is melted in adepressurized atmosphere and solidified to airtightly seal thethrough-hole 86 so that the inside of the package base 81 is maintainedin the depressurized state.

The crystal resonator 5 oscillates (resonates) at a predeterminedfrequency (for example, 32.768 kHz) when the crystal resonator element 1is excited by an external driving signal supplied through the externalconnection terminal 83.

As described above, since the crystal resonator 5 includes the crystalresonator element 1, it is possible to provide a crystal resonatorhaving the same effects (improvement in the Q value, for example) as thefirst embodiment.

Even when any one of the crystal resonator elements 2, 3, and 4 is usedin place of the crystal resonator element 1, the crystal resonator 5 canprovide the effects corresponding to the crystal resonator elements 2,3, and 4.

Third Embodiment

Next, an oscillator having the crystal resonator element described abovewill be described as a third embodiment.

FIGS. 7A and 7B are schematic diagrams showing a simplifiedconfiguration of an oscillator according to the third embodiment, inwhich FIG. 7A is a plan view, and FIG. 7B is a cross-sectional viewtaken along the line H-H in FIG. 7A. The electrodes of the crystalresonator element are not illustrated for better understanding of thedrawings.

A crystal oscillator 6 as an oscillator has a configuration in which thecrystal resonator 5 described above further includes a circuit element.The same portions as the crystal resonator 5 will be denoted by the samereference numerals, and description thereof is omitted.

As shown in FIGS. 7A and 7B, the crystal oscillator 6 includes thecrystal resonator element 1 of the first embodiment, an IC chip 91 as acircuit element having an oscillation circuit that oscillates thecrystal resonator element 1, and the package 80 that accommodates thecrystal resonator element 1 and the IC chip 91.

The IC chip 91 is attached to the bottom of the package base 81 and isconnected to other wirings by metal wires 92 such as Au or Al.

The crystal oscillator 6 oscillates (resonates) at a predeterminedfrequency (for example, 32.768 kHz) when the crystal resonator element 1is excited by a driving signal supplied from the oscillation circuit ofthe IC chip 91.

As described above, since the crystal oscillator 6 includes the crystalresonator element 1, it is possible to provide a crystal oscillatorhaving the same effects (improvement in the Q value, for example) as thefirst embodiment.

Even when any one of the crystal resonator elements 2, 3, and 4 is usedin place of the crystal resonator element 1, the crystal oscillator 6can provide the effects corresponding to the crystal resonator elements2, 3, and 4.

Fourth Embodiment

Next, an electronic device having the crystal resonator elementdescribed above will be described as a fourth embodiment. FIG. 8 is aschematic perspective view showing an electronic device of the fourthembodiment.

As shown in FIG. 8, a portable phone 700 as the electronic deviceincludes the crystal resonator 5 or the crystal oscillator 6 having thecrystal resonator element (1 or the like) described above as a timingdevice, for example, and further includes, a liquid crystal display 701,a plurality of operation buttons 702, an ear piece 703, and a mouthpiece 704.

The crystal resonator 5 and the crystal oscillator 6 described above canbe advantageously used as a timing device for electronic books, personalcomputers, televisions, digital cameras, video camcorders, videorecorders, car navigators, pagers, electronic notebooks, electroniccalculators, word processors, workstations, video phones, POS terminals,apparatuses having touch panels, and the like without being limited tothe portable phone. In any case, the effects described in the respectiveembodiments and the respective modifications can be obtained, and theoperation properties of these electronic devices can be improved.

In the respective embodiments and the respective modifications, thesupporting portion 15 and the weight portion 17 of each of the crystalresonator elements 1, 2, 3, and 4 may not be provided.

In the respective embodiments and the respective modifications, althoughthe weight portion 17 of each of the crystal resonator elements 1, 2, 3,and 4 has a structure such that it is disposed closer to the tip end ofeach of the resonating arms 12 and 13 than the arm portion 16 and has alarger width than the arm portion 16, the structure of the weightportion 17 is not limited to this but the weight portion 17 having adifferent structure can be also used.

For example, a weight portion 17 which is disposed closer to the tip endthan the arm portion 16 of the pair of resonating arms 12 and 13 andwhich has a thickness larger than that of the arm portion 16 can be alsoused. Moreover, a weight portion 17 which is disposed closer to the tipend than the arm portion 16 and in which a member (for example, a memberformed of a metal such as Au or Cu) formed of a material having a massdensity higher than that of the base materials of the crystal resonatorelements 1, 2, 3, and 4 is fixed or embedded can be also used.

The supporting portion 15 is not limited to a pair of supportingportions but may be provided in only one side.

In the respective embodiments and the respective modifications, althoughthe groove 18 has the bottom portion 18 c, the first side surface 18 a,and the second side surface 18 b and has a so-called H-shape incross-sectional view, the shape of the groove 18 is not limited to this.For example, a groove having a so-called V-shape in cross-sectional viewwhich has no bottom portion, and in which the first and second sidesurfaces are connected to make an acute angle can be also used.

In the respective embodiments and the respective modifications, althoughthe groove 18 is provided on both principal surfaces 10 a and 10 b ofthe resonating arms 12 and 13, the invention is not limited to this, andthe groove 18 may be provided on only one of the principal surfaces (10a or 10 b).

Moreover, in the respective embodiments and the respectivemodifications, although the number of resonating arms 12 and 13 has beendescribed to be one pair (two), the number of resonating arms is notlimited to this but may be one, or three or more.

Furthermore, in the respective embodiments and the respectivemodifications, although the flexural resonator element is formed of aquartz crystal, the invention is not limited to this. For example, theflexural resonator element may be formed of a piezoelectric materialsuch as lithium tantalate (LiTaO₃), lithium tetraborate (Li₂B₄O₇),lithium niobate (LiNbO₃), lead zirconate titanate (PZT), zinc oxide(ZnO), or aluminum nitride (AlN); or a silicon having a piezoelectricmaterial such as zinc oxide (ZnO) or aluminum nitride (AlN) as a coatingthereof.

The entire disclosure of Japanese Patent Application No. 2010-156576,filed Jul. 9, 2010 is expressly incorporated by reference herein.

What is claimed is:
 1. An oscillating piece comprising: a base; and aresonating arm that extends from the base along a first direction andhas a groove along the first direction on at least one of two principalsurfaces that are in a front and back relationship to each other,wherein an excitation electrode is disposed in the groove, theresonating arm includes a free end and a connection end with aconnection portion that is connected to the base at the connection end,a part of the groove is disposed in the connection portion, and the partof the groove includes a non-electrode region in which the excitationelectrode is not formed, the non-electrode region being closer to theconnection end than to the free end, the non-electrode ending across anentire width of the groove in the connection portion relative to asecond direction crossing the first direction.
 2. The oscillating pieceaccording to claim 1, wherein a width of the connection portion alongthe second direction crossing the first direction between an outer edgeof the groove and an outer edge of the resonating arm increases as itapproaches the base from the free end of the resonating arm.
 3. Theoscillating piece according to claim 1, wherein the principal surfaceshaving the groove sandwich an opening portion of the groove in plan viewand include a first principal surface and a second principal surface,the first principal surface being aligned along the second directioncrossing the first direction, an internal surface of the part of thegroove has a first side surface connecting with the first principalsurface and a second side surface connecting with the second principalsurface, the excitation electrode has a first excitation electrodeportion that is disposed on the first side surface and a secondexcitation electrode portion disposed on the second side surface, andthe non-electrode region is disposed between the first and secondexcitation electrode portions.
 4. The oscillating piece according toclaim 3, wherein on the internal surface of the part of the groove, thefirst excitation electrode portion is disposed on the entire surface ofthe first side surface, and the second excitation portion is disposed onthe entire surface of the second side surface.
 5. The oscillating pieceaccording to claim 3, wherein on the internal surface of the part of thegroove, the first excitation portion is disposed on part of the firstside surface, and the second excitation portion is disposed on part ofthe second side surface.
 6. The oscillating piece according to claim 1,wherein an internal surface of the part of the groove disposed in theconnection portion includes a sloped surface in which a depth of thegroove increases as it approaches the free end of the resonating armfrom the base, and wherein the non-electrode region is provided in thesloped surface.
 7. The oscillating piece according to claim 1, whereinthe resonating arm includes an arm portion that extends from a tip endof the connection portion, and a weight portion that extends from thetip end of the arm portion and whose width along the second directioncrossing the first direction is wider than the arm portion.
 8. Theoscillating piece according to claim 1, wherein the oscillating pieceincludes a plurality of the resonating arms.
 9. A resonator comprising:the oscillating piece according to claim 1, and a package thataccommodates the oscillating piece.
 10. An oscillator comprising: theoscillating piece according to claim 1, and a circuit.
 11. An electronicdevice comprising the oscillating piece according to claim
 1. 12. Theoscillating piece of claim 1, further comprising a support portion thatis connected to the base and is aligned with the resonating arm alongthe second direction crossing the first direction.
 13. The oscillatingpiece of claim 1, further comprising a pair of notch portions positionedon the base, each notch portion being aligned along the second directioncrossing the first direction.
 14. The oscillating piece according toclaim 1, wherein a portion of the non-electrode region closest to thefree end of the resonating arm is closer to the connection end than tothe free end.